Higher order Emden-Fowler type equations via uniform Haar Wavelet resolution technique
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Authors: Swati; Singh, Karanjeet; Verma, Amit K.; Singh, Mandeep
Abstract
A uniform Haar wavelet collocation based method is proposed for finding the numerical results for a class of third order nonlinear (Emden-Fowler type) singular differential equations with initial and boundary conditions. At the point of singularity, the coefficient of the such equation blows up, that causes difficulties in capturing the numerical solutions near the point of singularity. Haar wavelet approach handles this peculiar situation efficiently. The proposed method is employed to reduce the IVPs/BVPs into the system of algebraic equations and the nonlinearity is taken care by Newton-Raphson method. It is demonstrated that, the method is appropriate for both initial as well as boundary conditions as these conditions are taken care automatically. Some numerical examples have been illustrated in order to demonstrate the ease of implementation and applicability of the method. The L-2 norm and absolute errors further help to manifest the improvement of the findings with the increase in resolution J. We compare our results with other methods which exists in literature, e.g., variation iteration method (VIM), cubic B-spline method, Differential transformation method (DTM), Iterative decomposition method (IDM) and modified Adomian decomposition method (MADM). The second order convergence and error analysis of the proposed method is established to depict the accuracy and stability of the proposed method. (C) 2020 Elsevier B.V. All rights reserved.
Prevalence and Epidemiology of Multidrug-Resistant Pathogens in the Food Chain and the Urban Environment in Northwestern Germany
ANTIBIOTICS-BASEL
Authors: Klees, Sylvia; Effelsberg, Natalie; Stuhrenberg, Birgit; Mellmann, Alexander; Schwarz, Stefan; Kock, Robin
Abstract
The surveillance of antimicrobial resistance among humans and food-producing animals is important to monitor the zoonotic transmission of multidrug-resistant bacteria (MDRB). We assessed the prevalence of four MDRB within the meat production chain, including extended-spectrum beta-lactamase (ESBL)-producing, carbapenemase-producing Enterobacterales (CPE) and colistin-resistant Enterobacterales (Col-E), as well as vancomycin-resistant enterococci (VRE). In total, 505 samples from four stages of meat production, i.e., slaughterhouses, meat-processing plants, fresh food products and the urban environment, were collected in northwestern Germany in 2018/2019 and screened for the presence of MDRB using both culture-based and PCR-based techniques. We detected genes encoding for carbapenemases in 9-56% (bla(OXA-48), bla(KPC), bla(NDM), bla(VIM)) and colistin resistance-encoding mcr genes in 9-26% of the samples from all stages. Culture-based analysis found CPE and VRE only in environmental samples (11% and 7%, respectively), but Col-E and ESBL-producers in 1-7% and 12-46% of samples from all stages, respectively. Overall, our results showed that ESBL-producers and mcr-carrying Col-E were common in food-producing animals at slaughterhouses, in meat-processing plants and in food items at retail, while CPE and VRE were only found in the environment. The discrepancy between detected carbapenemase genes and isolated CPE emphasizes the need for more sensitive detection methods for CPE monitoring.